Chapter 5.2, Problem 11E

Exercises 9–14 require techniques from Section 3.1. Find the characteristic polynomial of each matrix, using either a cofactor expansion or the special formula for 3 × 3 determinants described prior to Exercises 15–18 in Section 3.1. [Note: Finding the characteristic polynomial of a 3 × 3 matrix is not easy to do with just row' operations, because the variable λ is involved.]

11. $\left[\begin{array}{ccc}4& 0& 0\\ 5& 3& 2\\ -2& 0& 2\end{array}\right]$